There is no mandatory requirement for immunizations to enter Tanzania unless a yellow fever vaccination is required under the following conditions
The government of Tanzania requires proof of yellow fever vaccination upon arrival ONLY if you are traveling from a country with risk of yellow fever. If you are traveling directly from the United States and transit through another country, it is NOT REQUIRED.
However if you will stay for more than 24 hours in a country that is endemic for Yellow Fever, you are required to have the vaccine. A complete list of these countries is available at the U.S. CDC website: https://www.cdc.gov/yellowfever/maps/index.html
Yellow Fever Vaccine Waiver:
If your doctor has recommended that you should not have the yellow fever vaccine due to a condition or having reached above 60 years of age, you can travel to Tanzania with your letter from the doctor and show it to the border immigration officer to waive the requirement.
Others: Vaccines commonly recommended for travelers to Africa include those against Tetanus, Diphtheria, Polio, Typhoid, Hepatitis A, Hepatitis B, Yellow fever, Malaria Rabies and Meningitis.
Certificate is required for entry into, or travel between, some African countries. Several of these vaccines require more than one dose, or take time to become effective. It is always best to seek advice from your doctor on immunization well in advance, if possible around 6 weeks before departure.